In order to simulate cryogenic H 2 − O 2 jets under subcritical condition, a numerical model is constructed to solve compressible reactive multi-component flows which involve complex multi-physics processes such as moving material interfaces, shock waves, phase transition and combustion. The liquid and reactive gaseous mixture are described by a homogeneous mixture model with diffusion transport for heat, momentum and species. A hybrid thermodynamic closure strategy is proposed to construct an equation of state (EOS) for the mixture. The phase transition process is modeled by a recent fast relaxation method which gradually reaches the thermo-chemical equilibrium without iterative process. A simplified transport model is also implemented to ensure the accurate behavior in the limit of pure fluids and maintain computational efficiency. Last, a 12-step chemistry model is included to account for hydrogen combustion. Then the developed numerical model is solved with the finite volume method where a low dissipation AUSM (advection upstream splitting method) Riemann solver is extended for multi-component flows. A homogeneous reconstruction strategy compatible with the homogeneous mixture model is adopted to prevent numerical oscillations across material interfaces. Having included these elements, the model is validated on a number of canonical configurations, first for multi-phase flows, and second for reactive flows. These tests allow recovery of the expected behavior in both the multiphase and reactive limits, and the model capability is further demonstrated on a 2D burning cryogenic H 2 − O 2 jet, in a configuration reminiscent of rocket engine ignition.